YES

Proof:
This system is quasi-decreasing.
By \cite{O02}, p. 214, Proposition 7.2.50.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to U(R).
Call external tool:
ttt2 - trs 30
Input:
  ?1(a, x) -> x
  f(x) -> ?1(x, x)
  ?2(B, x) -> C
  g(x) -> ?2(A, x)
  A -> B

 DP Processor:
  DPs:
   f#(x) -> ?1#(x,x)
   g#(x) -> A#()
   g#(x) -> ?2#(A(),x)
  TRS:
   ?1(a(),x) -> x
   f(x) -> ?1(x,x)
   ?2(B(),x) -> C()
   g(x) -> ?2(A(),x)
   A() -> B()
  TDG Processor:
   DPs:
    f#(x) -> ?1#(x,x)
    g#(x) -> A#()
    g#(x) -> ?2#(A(),x)
   TRS:
    ?1(a(),x) -> x
    f(x) -> ?1(x,x)
    ?2(B(),x) -> C()
    g(x) -> ?2(A(),x)
    A() -> B()
   graph:
    
   Qed